New linearization and reweighting for simulations of string sigma-model on the lattice

We study the discretized worldsheet of Type IIB strings in the Gubser-Klebanov-Polyakov background in a new setup, which eliminates a complex phase previously detected in the fermionic determinant. A sign ambiguity remains, which a study of the fermionic spectrum shows to be related to Yukawa-like terms, including those present in the original Lagrangian before the linearization standard in a lattice QFT approach. Monte Carlo simulations are performed in a large region of the parameter space, where the sign problem starts becoming severe and instabilities appear due to the zero eigenvalues of the fermionic operator. To face these problems, simulations are conducted using the absolute value of a fermionic Pfaffian obtained introducing a small twisted-mass term, acting as an infrared regulator, into the action. The sign of the Pfaffian and the low modes of the quadratic fermionic operator are then taken into account by a reweighting procedure of which we discuss the impact on the measurement of the observables. In this setup we study bosonic and fermionic correlators and observe a divergence in the latter, which we argue - also via a one-loop analysis in lattice perturbation theory - to originate from the U(1)-breaking of our Wilson-like discretization for the fermionic sector

Strings on the lattice and AdS/CFT

We present a new auxiliary field representation for the four-fermi term of the gauge-fixed Green-Schwarz superstring action which describes fluctuations around the null-cusp background in $AdS_5\times S^5$. We sketch the main features of the fermionic operator spectrum, identifying the region of parameter space where the sign ambiguity is absent. Measurements for the observables in the setup here described are presented and discussed in a forthcoming publication

Green-Schwarz superstring on the lattice

We consider possible discretizations for a gauge-fixed Green-Schwarz action of Type IIB superstring. We use them for measuring the action, from which we extract the cusp anomalous dimension of planar N=4 SYM as derived from AdS/CFT, as well as the mass of the two AdS excitations transverse to the relevant null cusp classical string solution. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and two Wilson-like fermion discretizations, one of which preserves the global SO(6) symmetry the model. We compare our results with the expected behavior at various values of g=λ√4π . For both the observables, we find a good agreement for large g, which is the perturbative regime of the sigma-model. For smaller values of g, the expectation value of the action exhibits a deviation compatible with the presence of quadratic divergences. After their non-perturbative subtraction the continuum limit can be taken, and suggests a qualitative agreement with the non-perturbative expectation from AdS/CFT. Furthermore, we detect a phase in the fermion determinant, whose origin we explain, that for small g leads to a sign problem not treatable via standard reweigthing. The continuum extrapolations of the observables in the two different discretizations agree within errors, which is strongly suggesting that they lead to the same continuum limit. Part of the results discussed here were presented earlier in [1]

Better Jet Clustering Algorithms

We investigate modifications to the $k_\perp$-clustering jet algorithm which preserve the advantages of the original Durham algorithm while reducing non-perturbative corrections and providing better resolution of jet substructure. We find that a simple change in the sequence of clustering (combining smaller-angle pairs first), together with the `freezing' of soft resolved jets, has beneficial effects.Comment: 32 pages, 16 figures, LaTeX2e, uses JHEP.cls (included). Version to be published in JHEP: reference to LUCLUS algorithm added. Program available at http://www.hep.phy.cam.ac.uk/theory/webber/camjet

Linear and nonlinear optical characteristics of the Falicov-Kimball model

We calculate the linear and nonlinear optical properties of the Falicov-Kimball model for a mixed-valent system within the self-consistent mean-field approximation. Second-harmonic generation can only occur if the mixed-valent state has a built-in coherence between the itinerant d-electrons and the localized f-holes. By contrast, second-harmonic generation cannot occur for solutions of the model with f-site occupation as a good quantum number. As an experimental test of coherence in mixed-valent compounds we propose a measurement of the dynamic second-order susceptibility.Comment: 4 pages, 2 PostScript figures, to appear in Physical Review Letter

Lattice and string worldsheet in AdS/CFT: a numerical study

We consider a possible discretization for the gauge-fixed Green-Schwarz (two-dimensional) sigma-model action for the Type IIB superstring and use it for measuring the cusp anomalous dimension of planar $\mathcal{N}=4$ SYM as derived from string theory. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and a Wilson-like fermion discretization. In this preliminary study, we compare our results with the expected behavior for very large values of $g=\frac{\sqrt{\lambda}}{4\pi}$, which is the perturbative regime of the sigma-model, and find a qualitative agreement at finite lattice spacing. For smaller $g$ the continuum limit is obstructed by a divergence. We also detect a phase in the fermion determinant, whose origin we explain, which for small $g$ leads to a sign problem not treatable via standard reweigthing. Results presented here are discussed thoroughly in~\cite{toappear}

Fitness Conferred by BCR-ABL Kinase Domain Mutations Determines the Risk of Pre-Existing Resistance in Chronic Myeloid Leukemia

Chronic myeloid leukemia (CML) is the first human malignancy to be successfully treated with a small molecule inhibitor, imatinib, targeting a mutant oncoprotein (BCR-ABL). Despite its successes, acquired resistance to imatinib leads to reduced drug efficacy and frequent progression of disease. Understanding the characteristics of pre-existing resistant cells is important for evaluating the benefits of first-line combination therapy with second generation inhibitors. However, due to limitations of assay sensitivity, determining the existence and characteristics of resistant cell clones at the start of therapy is difficult. Here we combined a mathematical modeling approach using branching processes with experimental data on the fitness changes (i.e., changes in net reproductive rate) conferred by BCR-ABL kinase domain mutations to investigate the likelihood, composition, and diversity of pre-existing resistance. Furthermore, we studied the impact of these factors on the response to tyrosine kinase inhibitors. Our approach predicts that in most patients, there is at most one resistant clone present at the time of diagnosis of their disease. Interestingly, patients are no more likely to harbor the most aggressive, pan-resistant T315I mutation than any other resistance mutation; however, T315I cells on average establish larger-sized clones at the time of diagnosis. We established that for patients diagnosed late, the relative benefit of combination therapy over monotherapy with imatinib is significant, while this benefit is modest for patients with a typically early diagnosis time. These findings, after pre-clinical validation, will have implications for the clinical management of CML: we recommend that patients with advanced-phase disease be treated with combination therapy with at least two tyrosine kinase inhibitors